SOLUTION: I need to solve this radical equation using the power principle. Problem: {{{sqrt(x+7)-2=sqrt(x-9)}}} I can work the other problems pretty easily, but they all have numbers befor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to solve this radical equation using the power principle. Problem: {{{sqrt(x+7)-2=sqrt(x-9)}}} I can work the other problems pretty easily, but they all have numbers befor      Log On


   

Question 288376: I need to solve this radical equation using the power principle.
Problem: sqrt%28x%2B7%29-2=sqrt%28x-9%29
I can work the other problems pretty easily, but they all have numbers before the x (ie sqrt%282x-9%29, so I can understand them a little better.
This one is throwing me for a loop.
I tried,
sqrt%28x%2B7%29=2%2Bsqrt%28x-9%29
and got
%28sqrt%28x%2B7%29%29%5E2=%282%2Bsqrt%28x-9%29%29%5E2
which gave me
x%2B7=%284%2B2sqrt%28x-9%29%2B%28x-9%29%29
so I moved the x%2B9 to the right side and came up with
0x-2=4%2B2sqrt%28x-9%29
then i subtracted the 4 from the right and moved it to the left to isolate my final radical and got
%28-2%29%2B%28-4%29=2sqrt%28x-9%29
which came to -6=2sqrt%28x-9%29
and then i squared each side again
%28-6%29%5E2=%282sqrt%28x-9%29%29%5E2
and got 26=4x-36
which is 1476-4x=0
Since there is no x%5E2 or a simple 2x or something, I can't seem to figure out how I would do this problem. Either I messed up the steps somewhere or this problem is unsolvable. I'm pretty sure I just confused a step or missed one all together.
Please help? This is due on Tuesday and I still have another 34 problems (out of 118) left. Almost done!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I need to solve this radical equation using the power principle.
Problem: sqrt%28x%2B7%29-2=sqrt%28x-9%29
I can work the other problems pretty easily, but they all have numbers before the x (ie sqrt%282x-9%29, so I can understand them a little better.
This one is throwing me for a loop.
I tried,
sqrt%28x%2B7%29=2%2Bsqrt%28x-9%29
and got
%28sqrt%28x%2B7%29%29%5E2=%282%2Bsqrt%28x-9%29%29%5E2
When you FOILed the right side, you should get
x + 7 = 4+%2B+4sqrt%28x-9%29+%2B+%28x-9%29
:
x + 7 = x+-+5+%2B+4sqrt%28x-9%29%29
:
x - x + 7 + 5 = 4sqrt%28x-9%29
:
12 = 4sqrt%28x-9%29
:
Square both sides and you have
144 = 16(x-9)
Divide both sides by 16
9 = x - 9
9+9 = x
x = 18
;
:
Check solution in original problem
sqrt%2818%2B7%29-2=sqrt%2818-9%29
sqrt%2825%29-2=sqrt%289%29